The number of delinquent loans at 16 major federal agencies rose 41 percent during the past fiscal year because of hard economic times and an attitude that people don't have to repay the government, an administration official said yesterday.

Joseph R. Wright, deputy director of the Office of Management and Budget, said a study showed that one out of every five dollars owed the 16 agencies--including the Agriculture, Education and Housing and Urban Development departments, the Small Business Administration and the Internal Revenue Service--is currently delinquent.

Overall, Wright said, individuals, communities and companies owe the federal government $260 billion in direct loans, not counting loan and credit guarantees or foreign debts. He said $38.4 billion of that amount is overdue.

The increase in delinquencies comes amid a drive by the administration to collect on overdue government loans.The effort has recouped $2.1 billion that otherwise would not have been collected, Wright said, based on reports from the 16 agencies. The delinquencies, he added, "could have been much worse if the administration would not have instituted an all-out push last year . . . to solve the problem."

Wright said the agencies recovered $46.6 billion this year compared to the $37.9 billion collected in fiscal 1981. Based on last year's rate, Wright said, the agencies would have collected only $44.5 billion this year without the administration's special efforts.

Wright said the administration should be credited for that extra $2.1 billion in collections because he couldn't "see any other reason" for it.

In April, 1981, President Reagan ordered agency heads to make debt collection a priority by hiring outside collectors when feasible, writing tougher regulations to control delinquency rates and giving overdue accounts to the Justice Department for prosecution.

The president's plan has encountered some problems. The Education Department hired outside collectors and reduced its own collection staff after an internal report said the private firms could collect loans as cheaply as agency employes could. But so far the two companies hired by the agency have recouped only about 7.8 percent of the $510 million in delinquent accounts given them. The department had projected a 10 percent collection rate.

William Inglehart of GC Services Corp., one of the firms, said his company was having trouble achieving that rate because the debts were too old and the Justice Department didn't have enough manpower to prosecute smaller cases.

Inglehart asked Education Secretary Terrel H. Bell to consider hiring private attorneys to file civil suits against debtors rather than relying on Justice. Without the threat of litigation, Inglehart said, a debt collector is like a "soldier operating without a rifle."

Wright said yesterday that OMB supports the idea of using private attorneys.

The Health and Human Services Department also has run into opposition from colleges that have been ordered to improve their student loan delinquency rates or be dropped from the federal programs.

But overall, Wright said, the debt collection campaign is running smoothly.

Until recently, most of the government's collection effort has been focused on debts owed by individuals. However, the Interior Department recently announced that it had hired Dun & Bradstreet Inc., the business credit rating service, to try to collect $5 million in overdue reclamation fees owed by coal mining companies. Dun & Bradstreet will keep 17 percent of what it collects.